Question

If x minus y equals to 4 and x y equal to 21 then find the value of x cube minus y cube

Answer 1

Step-by-step explanation:

$given \: x - y = 4 \: and \: xy = 21 \\ \\ cubing \: both \: sides\:of \: x - y = 4\\ {(x - y)}^{3} = {4}^{3} \\ {x}^{3} - {y}^{3} - 3xy(x - y) = 64 \\ {x}^{3} - {y}^{3} - 3 \times 21 \times 4 \: = 64 \\ {x}^{3} - {y}^{3} -252= 64 \: \\ {x}^{3} - {y}^{3} = 64 + 252 \\ {x}^{3} - {y}^{3} = 316$

Answer 2

The value of x^3-y^3 are -370 or 316

Step-by-step explanation:

Given Equations: $x-y = 4$  --- 1

                           $xy=21$ ---2

Substitute the value of x from 2 in 1

$x-y = 4$

$\frac{21}{y}-y=4$

$21-y^2=4y$

$y^2-21+4y=0$

$(y-3)(y+7)=0$

$y=3,-7$

Substitute the value of x in 1

At y = 3

x-y = 4

x-3=4

x= -7

So, $x^3-y^3=(-7)^3-3^3=-370$

At y=-7

x-(-7) = 4

x+7=4

x= 4-7

x= -3

So,$x^3-y^3=(-3)^3-(-7)^3=316$

Hence  the value of x^3-y^3 are -370 or 316

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